供参考。
-π/2≤a≤0-π/3≤a+π/6≤π/6cos（a+π/6）=根号（1-sin²）=3/5cosa=cos【（a+π/6）-π/6】=cos(a+π/6)cosπ/6+sin(a+π/6)sinπ/6=3/5×根号3/3-4/5×1/2=根号3/5-2/5=（根号3-2）/5
